Control

Control is a fundamental term of Fauceir Theory. Control is an elementary process defined as any change in outcome of an other process that is different from a mere random one.
This definition implies:

1. control can only be defined statistically,
2. control is controlled or in other words may be subdivided into more elementary control processes as all fauceirs are nested by definition.

This definition is in contrast to the common definition of control for two aspects.

1. In colloquial language, the term control is biased. We use to call the desired outcome the controlled one and the not desired outcome is the uncontrolled; or it is even called an accident.
2. In control theory, the term control is rather confined to a system that maintains a certain state. In fauceir theory this is rather called regulation as it involves feedback and hence a chain of control processes.These points represent special cases that are discussed below.

Thought experiment

The essence of fauceir control is illustrated in the following pictures. The first picture shows an abstract experiment without control. When the blue balls rain down both funnels A and B will receive the same amount as the clouds are identical.

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... while in the second one some control is exerted by the tilted bar. Although the clouds are still identical the A funnel will receive more blue balls as the bar directs some of the balls above the B funnel to the A funnel. The probabilities p(A) and p(B) are identical to the number of balls in funnel A and B respectively.

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Graphical representation

The first graph shows a process that has mainly tree possible outcomes. Without control the outcome b2 is most likely.

The second graph shows the same process that again has the same tree possible outcomes. With control the outcome b1 is most likely.